Question

Verify that the following numbers represent Pythagorean triplet:
(i) 12, 35, 37
(ii) 7, 24, 25
(iii) 27, 36, 45
(iv) 15, 36, 39

Answer 1

We will check for a Pythagorean triplet by checking if the square of the largest side is equal to the sum of the squares of the other two sides.

$$\begin{gathered} \left(\mathrm{i}\right){37}^2=1369 \\ {12}^2+{35}^2=144+1225=1369 \\ {12}^2+{35}^2={37}^2 \\ \mathrm{Yes},\mathrm{they}\mathrm{represent}\mathrm{a}\mathrm{Pythagorean}\mathrm{triplet}. \\ \left(\mathrm{ii}\right){25}^2=625 \\ {7}^2+{24}^2=49+576=625 \\ {7}^2+{24}^2={25}^2 \\ \mathrm{Yes},\mathrm{they}\mathrm{represent}\mathrm{a}\mathrm{Pythagorean}\mathrm{triplet}. \\ \left(\mathrm{iii}\right){45}^2=2025 \\ {27}^2+{36}^2=729+1296=2025 \\ {27}^2+{36}^2={45}^2 \\ \mathrm{Yes},\mathrm{t}\mathrm{hey}\mathrm{represent}\mathrm{a}\mathrm{Pythagorean}\mathrm{triplet}. \\ \left(\mathrm{iv}\right){39}^2=1521 \\ {15}^2+{36}^2=225+1296=1521 \\ {15}^2+{36}^2={39}^2 \\ \mathrm{Yes},\mathrm{they}\mathrm{represent}\mathrm{a}\mathrm{Pythagorean}\mathrm{t}\mathrm{riplet}. \end{gathered}$$